"Thus according to the latter observers, the density at 100 [℃] is 0.0006187 [g/m3]."

0.6 kg/m3

Water, while remarkable in its liquid form, becomes immensely more useful as a gas. Steam was the footing of the Industrial Revolution. With the invention and refinement of the steam engine many possibilities were created. In 1912, steam drove the Titanic, and is still used to power ships today. Smaller steam engines were used in factories and helped ramp up production. Today, perhaps even more importantly steam is used in the production of electricity; Nuclear power heats water into steam which rotates a turbine. The turbine spins a generator which makes electric current. This is where the density of steam comes in handy. Higher differences in density will cause a turbine to spin faster, and in turn be more powerful.

Steam also has some more exotic uses. The television show Mythbusters created a steam cannon, and while it was less than powerful, it was a successful proof of concept. The Mythbusters used steam at a much higher temperature than the boiling point; however, our daily interaction with steam happens at 100 °C and 1 atm, where it has a density of 0.6 kg/m3. This interaction is not high-tech or complicated, and we usually take it for granted. Steam causes that signature whistle that lets one know, tea is ready.